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Rigorous and Portable Standard Functions

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Abstract

Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

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  1. Institute of Compute Science III, Technical University Hamburg-Harburg, Schwarzenbergst. 95, 21071, Hamburg, Germany

    Siegfried M. Rump

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  1. Siegfried M. Rump
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Rump, S.M. Rigorous and Portable Standard Functions. BIT Numerical Mathematics 41, 540–562 (2001). https://doi.org/10.1023/A:1021971313412

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